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In this article, we give two different sufficient conditions for theirreducibility of a polynomial of more than one variable, over the field ofcomplex numbers, that can be written as a sum of two polynomials which dependon mutually disjoint sets of variables. These conditions are derived fromanalyzing the Newton polytope of such a polynomial and then applying the`Irreducibility criterion' introduced by Gao.

Irreducibility of a sum of polynomials depending on disjoint sets of variables